Orlicz capacities and Hausdorff measures on metric spaces
2005 (English)In: Mathematische Zeitschrift, ISSN 0025-5874, Vol. 251, no 1, 131-146 p.Article in journal (Refereed) Published
In the setting of doubling metric measure spaces with a 1-Poincaré inequality, we show that sets of Orlicz Φ-capacity zero have generalized Hausdorff h-measure zero provided that ∫10Θ -1(t1-sh(t))dt< ∞ where Θ -1 is the inverse of the function Θ(t)=Φ(t)/t, and s is the "upper dimension" of the metric measure space. This condition is a generalization of a well known condition in R n . For spaces satisfying the weaker q-Poincaré inequality, we obtain a similar but slightly more restrictive condition. Several examples are also provided. © Springer-Verlag Berlin Heidelberg 2005.
Place, publisher, year, edition, pages
2005. Vol. 251, no 1, 131-146 p.
IdentifiersURN: urn:nbn:se:liu:diva-30246DOI: 10.1007/s00209-005-0792-yLocal ID: 15751OAI: oai:DiVA.org:liu-30246DiVA: diva2:251068